Neutrinoless Double Beta Decay(0𝜈𝛽𝛽) is one of the major research interests in neutrino physics. The discovery of 0𝜈𝛽𝛽 would answer persistent puzzles in the Standard Model of Elementary Particles. KamLAND-Zen is one of the leading efforts in the search of 0𝛽𝛽 and has acquired data from 745 kg of ^{136}Xe over 224 live-days. This data is analyzed using a Bayesian approach consisting of a Markov Chain Monte Carlo (MCMC) algorithm. The implementation of the Bayesian analysis, which is the focal point of this dissertation, yields a 90\% Credible Interval at T^{0𝜈}_{1/2} = 7.03 × 10^{25} years. Finally, a machine learning event classification algorithm, based on a spherical convolutional neural network (spherical CNN) was developed to increase the T^{0𝜈}_{1/2} sensitivity. The classification power of this algorithm was demonstrated on a Monte Carlo detector simulation, and a data driven classifier was trained to reject crucial backgrounds in the 0𝜈𝛽𝛽 analysis. After implementing the spherical CNN, an increase in T^{0𝜈}_{1/2} sensitivity of 11.0% is predicted. These early studies pave the way for substantial improvements in future 0𝜈𝛽𝛽 analyses.